Purpose: To investigate a computationally efficient method for optimizing the Cramér-Rao Lower Bound (CRLB) of quantitative sequences without using approximations or an analytical expression of the signal. Methods: Automatic differentiation was applied to Bloch simulations and used to optimize several quantitative sequences without the need for approximations or an analytical expression. The results were validated with in vivo measurements and comparisons to prior art. Multi-echo spin echo and DESPO1 were used as benchmarks to verify the CRLB implementation. The CRLB of the Magnetic Resonance Fingerprinting (MRF) sequence, which has a complicated analytical formulation, was also optimized using automatic differentiation. Results: The sequence parameters obtained for multi-echo spin echo and DESPO1 matched results obtained using conventional methods. In vivo, MRF scans demonstrate that the CRLB optimization obtained with automatic differentiation can improve performance in presence of white noise. For MRF, the CRLB optimization converges in 1.1 CPU hours for NTR = 400 and has O(NTR) asymptotic runtime scaling for the calculation of the CRLB objective and gradient. Conclusions: Automatic differentiation can be used to optimize the CRLB of quantitative sequences without using approximations or analytical expressions. For MRF, the runtime is computationally efficient and can be used to investigate confounding factors as well as MRF sequences with a greater number of repetitions.
- automatic differentiation
- Cramér-Rao lower bound
- magnetic resonance fingerprinting
- optimal experiment design
- quantitative imaging
ASJC Scopus subject areas
- Radiology Nuclear Medicine and imaging